American Geophysical Union Fall Meeting 2001
******************************************

Responses of Simulated and Natural Shorelines to High-Angle Waves: Perturbation Growth and Long-Range Interactions

Andrew Ashton and Brad Murray
Division of Earth and Ocean Sciences/Center for Nonlinear and Complex Systems
Duke University

A straight shoreline is unstable if waves approach the shore at high angles. This basic instability arises from the robust existence of a maximum in alongshore sediment transport (at a relative angle between deep-water wave crests and the shoreline of approximately 45 degrees). We have developed a simple numerical model to investigate the finite-amplitude, long-term behavior of this instability acting over an extended domain. Perturbations merge and grow for all simulations with random wave distributions weighted towards high-angle waves.

These growing perturbations interact both locally and over surprisingly large distances in ways that lead to the development of large-scale coastline features. When the wave-angle distribution is asymmetric, creating a net alongshore sediment flux, features translate in the downdrift direction. This behavior is similar to the development of various kinds of bedforms. Somewhat unexpectedly, amplitude and wavelength growth occurs for both symmetric and asymmetric wave distributions. As features become larger, growth can be discontinuous: quasi-stable shoreline configurations with almost equal amplitude and wavelength features can develop that occasionally experience rapid period doubling. (Features even slightly smaller than their neighbors are sheltered from the highest-angle waves, causing the larger neighboring features to grow relative to the smaller features. The smaller features will eventually experience a wave distribution weighted toward low-angle waves, resulting in the rapid disappearance of the smaller features and growth of their neighbors.) For asymmetrical wave distributions weighted heavily toward high-angle waves, spits grow at an angle to the overall shoreline trend, extending large distances from shore and sheltering a downdrift region from waves coming from the dominant direction. These spits interrupt the alongshore sediment transport; originally continuous littoral cells can be segmented by the self-organization of an unstable shoreline.

The development of simulated large-scale features changes local shoreline orientations and wave climates in ways that inhibit the long-term growth of smaller-scale perturbations. However, during storms producing waves at a high angle relative to the local shoreline orientation, the instability is expected to affect perturbations at a wide range of scales. This basic prediction may be related to erosion 'hot spots' and recent findings that some natural shorelines show changes occurring over all scales over a range extending to tens of kilometers. Short-term model results also exhibit such a power-law scaling.

Qualitatively, large-scale simulated shoreline shapes resemble a number of naturally occurring features, including alongshore sandwaves, angular spits (Sea of Azov) and cuspate forelands (Carolina Coast). Wind and wave data indicates that under current climactic conditions, these natural shorelines are subjected to a predominance of high-angle waves. Simulations calibrated to the wave climate at these locations show the development of similar shapes. The aspect ratio of simulated shapes is also investigated as a function of wave-distribution characteristics, and compared to natural shorelines. The numerical model indicates that this fundamental instability could be responsible for the self-organization of a wide variety of poorly understood large-scale shoreline phenomena.